A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Introduction to algorithms
Classical heuristics for the capacitated VRP
The vehicle routing problem
Algorithms for Capacitated Vehicle Routing
SIAM Journal on Computing
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
Improved Approximation Algorithms for the Uncapacitated Facility Location Problem
SIAM Journal on Computing
Approximation Algorithms for Metric Facility Location Problems
SIAM Journal on Computing
Approximation algorithms for group prize-collecting and location-routing problems
Discrete Applied Mathematics
Fifty Years of Vehicle Routing
Transportation Science
Scheduling trucks in cross-docking systems: Robust meta-heuristics
Computers and Industrial Engineering
A Branch-and-Cut method for the Capacitated Location-Routing Problem
Computers and Operations Research
An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem
SIAM Journal on Computing
The Design of Approximation Algorithms
The Design of Approximation Algorithms
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An approximation algorithm for an optimization problem runs in polynomial time for all instances and is guaranteed to deliver solutions with bounded optimality gap. We derive such algorithms for different variants of capacitated location routing, an important generalization of vehicle routing where the cost of opening the depots from which vehicles operate is taken into account. Our results originate from combining algorithms and lower bounds for different relaxations of the original problem; along with location routing we also obtain approximation algorithms for multidepot capacitated vehicle routing by this framework. Moreover, we extend our results to further generalizations of both problems, including a prize-collecting variant, a group version, and a variant where cross-docking is allowed. We finally present a computational study of our approximation algorithm for capacitated location routing on benchmark instances and large-scale randomly generated instances. Our study reveals that the quality of the computed solutions is much closer to optimality than the provable approximation factor.